A History of Geometrical Methods

by Julian Lowell Coolidge

Overview

Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.

Product Details

ISBN-13:	9780486158532
Publisher:	Dover Publications
Publication date:	02/27/2013
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	480
File size:	15 MB
Note:	This product may take a few minutes to download.

Table of Contents

I. Synthetic Geometry
1. The Beginnings of Geometry
2. Greek Mathematics
3. Later Elementary Geometry
4. The Non-Euclidean Geometries
5. Projective Geometry
6. Descriptive Geometry
II. Algebraic Geometry
1. The Beginnings of Algebraic Geometry
2. Extension of the System of Linear Coordinates
3. Other Systems of Point Coordinates
4. Enumerative Geometry
5. Birational Geometry
6. Higher Spaces and Higher Space Elements
7. Geometrical Transformations
III. Differential Geometry
1. Early Writers.
2. Intrinsic Geometry and Moving Axes
3. Gauss and the Classical Theory of Surfaces
4. Projective Differential Geometry
5. Absolute Differential Geometry, Epilogue. Index of Authors Quoted. Subject Index